CURVES IN HILBERT MODULAR VARIETIES

Erwan Rousseau (1) , Frédéric Touzet (2)

1 I2M - Institut de Mathématiques de Marseille
2 IRMAR - Institut de Recherche Mathématique de Rennes

We study curves in Hilbert modular varieties from the point of view of the Green-Griffiths-Lang conjecture claiming that entire curves in complex projective varieties of general type should be contained in a proper subvariety. In the first part, using holomorphic foliations theory, we establish the second main theorem in this context. In the second part, with a metric approach, we establish the strong Green-Griffiths-Lang conjecture for Hilbert modular varieties up to finitely many possible exceptions.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Erwan Rousseau, Frédéric Touzet. CURVES IN HILBERT MODULAR VARIETIES. 2015. ⟨hal-01103058v1⟩